Just tell them to look at time played..
Pretty sure the ban system is automated. But it's sophisticated and takes everything in your combat record into equation and if there is a des repent (as in its clear you boosted) you will get reset.
It's not to hard to understand how easy it is for a System like this to exist.
Treyarch do not use an automated banning system. Instead, there is a live security team who investigate reports using past gameplay footage from the reported player. The security team will take action if the player is found guilty of breaking any rules. Keep in mind, these are real people reviewing thousands upon thousands of reports so punishment will not be immediate. It can take anywhere from a couple weeks to a month for a player to be banned.
Since Treyarch do not use an automated banning system, don't worry about being banned after receiving an X amount of reports. Treyarch know there are players out there who are good and players out there who report them. If you are a legitimate player nothing bad will befall you.
Dan Amrich, the Community Manager at Activision, goes in a little more depth of how reports are handled: